Connecting stellar mass and star-formation rate to dark matter halo mass out to z ∼ 2

We have constructed an extended halo model (EHM) which relates the total stellar mass and star-formation rate (SFR) to halo mass (M_h). An empirical relation between the distribution functions of total stellar mass of galaxies and host halo mass, tuned to match the spatial density of galaxies over 0 < z < 2 and the clustering properties at z ∼ 0, is extended to include two different scenarios describing the variation of SFR on M_h. We also present new measurements of the redshift evolution of the average SFR for star-forming galaxies of different stellar masses up to z = 2, using data from the Herschel Multi-tiered Extragalactic Survey for infrared bright galaxies. Combining the EHM with the halo accretion histories from numerical simulations, we trace the stellar mass growth and star-formation history in haloes spanning a range of masses. We find that: (1) the intensity of the star-forming activity in haloes in the probed mass range has steadily decreased from z ∼ 2 to 0; (2) at a given epoch, haloes in the mass range between a few times 10^(11) M_⊙ and a few times 10^(12) M_⊙ are the most efficient at hosting star formation; (3) the peak of SFR density shifts to lower mass haloes over time; and (4) galaxies that are forming stars most actively at z ∼ 2 evolve into quiescent galaxies in today's group environments, strongly supporting previous claims that the most powerful starbursts at z ∼ 2 are progenitors of today's elliptical galaxies